Question

CSATMediumPrelims 2019Maths

Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is

What is the length of the original sheet of paper?

Explanation

Identify the odd prime numbers: Single-digit odd primes: 3, 5, 7
Find the average of these numbers: Average = $rac{ (3 + 5 + 7) }{3} = 5$ Length of the first piece = 5 units
Use the relations given in the problem: Second piece = first piece + one-third of the third piece Third piece = first piece + second piece
Set up equations: Let the lengths of the pieces be x (first), y (second), and z (third) $x = 5$ $y = x + (1/3)z$ $z = x + y$
Solve for the lengths: From $z = x + y$ , substitute $y = 5 + (1/3)z$ into it: $z = 5 + (5 + (1/3)z)$ Simplify to get: $z = 10 + (1/3)z$ Solve for z: $(2/3)z = 10 \rightarrow z = 15$
Find y: $y = 5 + (1/3) \cdot 15 = 10$
Total length: Total length = $x + y + z = 5 + 10 + 15 = 30$